Igen Tech Report

8/12/2019 Igen Tech Report

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Towards More Representative Internet Topologies

Bruno QuoitinINL - IP Networking Lab

CSE Dept, Universit Catholique de Louvain (UCL)Place St. Barbe 2, 1348 Louvain la neuve - Belgium

[email protected]

1. INTRODUCTIONIn this report, we discuss the parameters that are important for

the generation of synthetic topologies. We focus on the parametersthat are signicant for the evaluation of interdomain routing pro-tocols and interdomain trafc engineering, though this discussionalso largely applies to the evaluation of other protocols or applica-tions. Indeed, the evaluation of applications such as Voice/Videoover IP or peer-to-peer (P2P) software critically depends on theproperties captured by the topology model. For the Voice/Videoover IP protocol, the delay between participants as well as theirgeographic distribution are relevant. For P2P, the heterogeneity of link capacities has an impact on the performance [36]. In the caseof routing protocols and trafc engineering methods, another rele-vant property of the topology is the path diversity, i.e. the existenceof alternative paths between a source and a destination. These pathsmay have differing properties such as the delay, the available band-width or even the node- or edge-disjointness.

The problem of obtaining an accurate picture of the Internettopology is not new. We do not know the shape of the Internettoday, especially at the router level. There are multiple reasons forthis. First, we do not know about the internal structure of domainssince their operators are often reluctant to publish the topology of their network. The internal structure of a domain is important since

it constrains the paths that intradomain and interdomain routingprotocols will select. Second, we do not know how domains areconnected together. There is no map of the Internet available to-day. Looking at BGP routing tables from a small set of monitoringpoints [40] provides a gross picture of the interdomain graph. How-ever, this approach misses a large number of edges, mainly of theshared-cost type, that are valuable for interdomain routing proto-cols. In addition, the interdomain graph that we have today indi-cates when domains are connected together, but it does not provideinformation on the link redundancy. Finally, an important charac-teristic of the interdomain graph is the notion of policies. To theopposite of the intradomain graph, not all paths through the in-terdomain graph are allowed. These paths are constrained by thepolicies that are enforced by the domains. Hence, the edges of theinterdomain graph must be tted out with attributes dening therelationship [19] between the interconnected domains.

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Today, no topology generator is able to produce router-level topolo-gies of the Internet in a satisfactory way. In this chapter, we proposea methodology to build more realistic router-level topologies andwe apply it to the construction of an experimental Internet topol-ogy. We rst survey in Section 2, the approaches currently beingused by researchers to infer or generate Internet-like topologies.Second, we summarize in Section 3 what are the important charac-teristics of Internet topologies suitable for the evaluation of inter-domain routing protocols and trafc engineering techniques. Third,we describe our approach in Section 4. We start by describing howreal-world network toppologies are designed. We survey the met-rics that can be used to evaluate a network design. Then, we deneour methodology for building router-level topologies. In Section 5,we apply this methodology to the construction of an experimentalInternet topology. Finally, we conclude in Section 6.

2. RELATED WORKSeveralapproaches to the generation of Internet router-level topolo-

gies suitable for simulation have been proposed in the literature.The rst and most natural approach was to rely on existing network topologies. This approach is limited due to the difculty of ob-taining the topology of operational networks today. Most network operators still feel nervous when asked to reveal a precise view of their network topology. There has then been proposals for inferringnetwork topologies at the router-level from measurements. Rocket-fuel [38] is the most famous of these techniques and it relies on theresult of several traceroutes. Unfortunately, since traceroutes onlyperform a sampling of the real network topology, these techniquessometimes miss multiple paths between routers [26], [44]. In ad-dition, these techniques sometimes fail to resolve router aliases re-sulting in links and routers that do not really exist [44].

At the AS-level, techniques such as [40] have been proposedto infer the business relationships between domains from multi-ple BGP routing table dumps. These techniques also provide anundersampling of the real interdomain topology since BGP rout-ing tables only provide the best routes selected by BGP [2]. Thesetopologies are thus not representative of the actual diversity of the

AS-level paths. In [9], Willinger et al discuss the completeness of the inferred topologies based on local views. In addition, inferredAS-level topologies do not provide information on the number of peerings between domains nor information on the internal structureof domains. Other inferrence techniques have been proposed later,such as [4] and [12]. The later shows that using BGP updates morepeering links are discovered. However these techniques suffer fromthe same limitations as studied in [9].

Another approach consists in generating synthetic topologies shar-ing selected properties with the real Internet. Available generatorssuch as BRITE [29] and GT-ITM [8] produce topologies that re-


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spect graph properties seen in the real Internet. GT-ITM for in-stance allows to build router-level topologies with a backbone/accesshierarchy. Nodes are placed randomly on a map and connected us-ing a probabilistic model such as Waxman [47]. The problem of this approach is that topologies are generated in order to mimicpure graph properties of real networks. They fail to capture theoptimization process that is also at the basis of the real network topologies.

In [3], Alderson et al have presented a novel approach to the de-sign and generation of realistic Internet topologies which reposeson taking into account the economical and technical driving forcesof the Internet. Their idea consists in formulating the network de-sign problem as an optimization problem which takes as input atrafc demand and produces a router/host level topology. Later, in[27], Li et al have propsed new metrics for evaluating generatedtopologies. They have used their metrics to evaluate various gen-erated topologies and compare them to real networks and Heuris-tically Optimal Tradeoffs (HOT) networks [14] that have the samenode-degree distribution. They concluded that topologies gener-ated without taking into account economical and technical con-straints perform poorly. They also predicted that future topologygenerators should not be built on pure graph-theoretic propertiesbut upon more pragmatic properties such as the maximum through-

put that can be achieved by the network and its resilience to failures.

3. MOTIVATIONS AND REQUIREMENTSIn this section, we describe the key characteristics that a model

of the Internet topology should capture to be suitable for the eval-uation of interdomain routing and trafc engineering. These re-quirements cover both intradomain and interdomain characteristicsof the topology.

Realistic intradomain structure . Each domain in the In-ternet can be composed of several routers. The structure of the interconnection of these routers is an important charac-teristic of the Internet topology. There are different reasonsto take into account the intradomain structure of domains ina model of the Internet topology. First, the characteristics

of the intradomain paths such as the delay or the bandwidthare components of the interdomain paths characteristics. Theinternal structure of a domain must therefore include suchcharacteristics. Second, the paths available to cross a do-main inuence the selection of interdomain paths . With BGPfor instance, this interaction is known as hot-potato routing,i.e. BGP will prefer to cross the domain with the lowest IGPcost path. The paths used to traverse a domain will dependon the setting of the IGP weights. We showed in Chapter ??that in the GEANT network, a large number of routing deci-sions were based on the IGP cost. Finally, inside a domainthere are often multiple paths to go from an ingress point toan egress point. This diversity of available paths inuencesthe performance of trafc engineering techniques. The inter-nal structure of domains is thus an important component of arealistic model of the Internet topology.

Redundancy of interdomain links . Another relevant char-acteristic of the Internet topology is the availability of mul-tiple parallel links between two different domains. Internetdomains maintain multiplepeering links with their neighborsfor different reasons. A rst reason is the resilience of thepeering: if one link fails, the peering is still operational. Asecond reason is the ability to balance the trafc load accrossmultiple interdomain links, leading to an increased band-width . A third reason is the provision of egress points that

are closer to a given geographical area. Modeling multiplelinks between two domains is thus important for the evalua-tion of interdomain trafc engineering solutions. In currentapproaches such as BRITE, redundancy can occur acciden-taly while it is deliberate in the real world.

BGP sessions graph . The physical Internet topology is over-layed by a graph of BGP sessions. This graph has two im-portant characteristics that matter for the evaluation of inter-domain routing and trafc engineering. The rst one is thepresence of BGP policies on eBGP sessions. These policieswill constrain the authorized interdomain paths [19]. Thesecond characteristic is the graph of iBGP sessions withineach domain. The default graph is a clique, but it quicklybecomes too large when the number of routers in the do-main grows. For this reason, hierarchical iBGP topologieshave been introduced. These topologies rely on the utiliza-tion of route-reectors. The introduction of route-reectorsin an iBGP topology change can cause important changes inthe selection of interdomain routes. Typically, small domainswill use a full-mesh of iBGP sessions while larger domainswill organize their iBGP topology around route-reectors.

Geographical location of routers . The geographical loca-tion of routers is another important characteristic of the In-ternet topology. There is a strong correlation between the lo-cation of the routers and the location of urban and industrialareas [25]. The Points of Presence (PoPs) of a domain willoften be located in such places. The location of routers hasan impact on their interconnection, i.e. on the intradomaintopology structure. It also has an impact on the propagationdelay along the links that interconnect the routers. Anotheraspect of the geographical spread of routers is the geograph-ical coverage of Internet domains . Some domains cover asmall region while others, such as large international transitnetworks, can span multiple countries or continents. A lasteffect of the geographical location of routers is the locationof the interdomain peering links . Indeed, two domains will

often establish their peering links at places where they bothhave equipment.

4. ROUTER-LEVEL TOPOLOGIESIn thissection, wepresent a new approach to the design of router-

level network topologies. Our approach relies on the use of network design heuristics. The chapter is organized as follows. We will rstdiscuss in Section 4.1 the problem of network design. Basically,real world networks are the outcome of an optimization process butthey also follow operational guidelines. We identify the objectivesfollowed by a a real world network designer in practice. Then, wedene in Section 4.2 a set of metrics that can be used to evaluate theperformance of networks as well as to compare different network designs together. We apply a subset of these metrics on a set of

real networks in Section 4.3 to show that real networks sample thespectrum of several design parameters. Finally, we describe ourdesign methodology in Section 4.4.

4.1 Network designReal world networks are the outcome of a careful design pro-

cess. The network design problem consists of multiple, sometimescontradictory objectives. No single optimal solution exists, rather afront of possible solutions. The network design problem has beenfairly discussed in the literature, in particular by [6, 21]. The objectives of network design may be summarized in minimizing the


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latency , dimensioning the links so that the trafc can be carriedwithout congestion, adding redundancy so that rerouting is possi-ble in case of link or router failure and, nally, the network must bedesigned at the minimum cost . None of these objectives are cur-rently explicitly found in degree-based generators such as BRITE[29] or GT-ITM [7].

Usually, a network designer knows the set of nodes that are to beinterconnected as well as a prediction of the trafc demand betweenthese nodes. It will then use network design tools such as CaridenMATE [42], Delite [6], WANDL IP/MPLSView [24] or OPNETSPGuru [43] to build a network design that will accomodate thetrafc demand. Designing a good network is a time-consuming task though. Indeed, designing an optimal network is computationalyexpensive. Its complexity is roughly evaluated to O (n 5 ) by [21].This is the reason why network design often relies on heuristics.In addition, the network designer must go through many possibleinstances of a network design until its objectives are reached andhis budget can accomodate it.

Real world networks are often designed with additional con-straints in mind. For instance, routers have a maximum degree thatcorresponds to the maximum number of interfaces they can sup-port [27]. Core routers for instance have an high bandwidth buta limited number of interfaces. In constrast, distribution and ac-

cess routers can support a larger number of interfaces but their totalbandwidth is lower. This leads to a 2- or 3-levels network hierar-chy with an increasing aggregation of trafc in the top (core) level.Topology generators such as BRITE or GT-ITM will tend to pro-duce networks with high degree nodes (hubs) in the core. Anotherpragmatic constraint to the design of a network can be the avail-ability of rack space or power supply in a colocation. In additionto this, network designers apply design guidelines [37], mainly forthe design of robust networks. An interesting point to note is thata book such as [37] contains no maths at all. In practice, network design is thus not only an optimization problem.

4.2 Network metricsIn order to measure topologies of real networks as well as to

compare topologies generated by network design heuristics, we

have selected a set of metrics from the networking literature ([5]is a fair reference). With the following metrics, we capture vari-ous aspects of the network design problem. The metrics cover per-formance properties (delay, redundancy), network design cost andpure graph properties. We use standard graph-theoretic notions.Specically, let G (V, E , w ) be a weighted graph. V is the set of vertices (or nodes) of G and E is the set of edges. The w is theedge weighting function w : E R .

1. Distance distribution: A rst metric is the distribution of the distances between pairs of nodes along the shortest-path route. It is an indication of the delay required to transmitpackets between these nodes under the assumption that thelargest part of the transmission delay is due to the propaga-tion delay along the links. In particular, the network diame-ter is the length of the longest shortest path. We measure thedistribution of the distances between pairs by measuring thelength of the shortest-paths between all pairs of nodes.

2. Path diversity: To measure the amount of redundancy of-fered by a network, we use the path diversity . This met-ric measures the availability of diverse paths between pairsof nodes. The availability of diverse paths is important fornetwork robustness and trafc engineering. We compute thepath diversity of G in the following way. For each pair of distinct vertices i and j taken in V , we compute the path di-

versity (i, j ) by counting the number of edge-disjoint pathsthat are available from i to j . First, we compute the shortest-path ij from i to j using the edges in E . Then we removethe edges of ij from E and compute another shortest-path.This shortest-path will be edge-disjoint from the rst one.We continue until no new path can be found. We repeatthis for each pair (i, j ). A similar metric was used in [44]to compare the path diversity of the Sprint network and thetopologies inferred by Rocketfuel [38].

3. Connectivity: Another way to measure the redundancy of a network is to compute the k-edge-connectivity [39]. Thismetric gives the size of a minimum cut in the network. Com-pared to the path-diversity metric described in the above para-graph, the k-edge-connectivity only gives a lower bound onthe number of diverse paths for all the pairs of nodes. To theopposite, the path-diversity metric gives a lower bound foreach individual pair.

4. Node degree: The distribution of the node degrees is a met-ric which is frequently used to evaluate network topologies.This distribution informs on the existence of hubs, which arenodes with a high degree, where many other nodes connect.It is commonly admitted that networks have a small num-ber of nodes with an high degree (in the backbone) and alarge number of nodes with a low degree (access nodes). Ithas been shown that for some networks, this distribution fol-lows a power law [15]. An interesting fact is that, accordingto [21], the average node degree of North American carriernetworks, is d < 2.5, while the average node degree of Eu-ropean networks is closer to d > 3.5. The reason is that inNorth America, networks span large distances with relativelysparse population in some areas. In addition, North Ameri-can networks have more often performed economies of scaleby using increased capacity links.

5. Centrality: The betweenness-centrality [5] is a measure of the centrality of vertices or edges in the graph. It basically

computes the amount of shortest-paths that go through a ver-tex or an edge. The centrality of a vertex v is computed as

c(v) = Xs = v = t st (v)

st

i.e. the sum for all pairs of sources and destination (s, t ) of the fraction of shortest-paths from s to t that pass throughv . st denotes the number of shortest-paths from s to t and st (v) denotes the number of shortest-paths from s to t thatgo through v. A similar denition is used to compute thecentrality of edges. Here, the direction of the edges is takeninto account.

c(u, v ) =

Xs = u,v st (u, v )

st

6. Network cost: Finally, an important operational constraintis the limited amount of money available to build the net-work. It is however difcult to dene a network cost metric.The cost of a network design is difcult to evaluate sinceit depends on the technology used for links and routers, thebandwidth of links and their length. Though, it is possibleto get an idea of some components of the network cost. Forinstance, the network span gives an idea of the total lengthof the network links.


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Mesh-topologygeneration

Input:- set of nodes- [traffic demand] Grouping

into PoPs

IGP weights[and capacities]

assignment

Figure 1: Network design methodology.

to other backbone routersin other PoPs

PoP

Backbonepart

Distributionpart

Figure 2: Structure of a PoP ( n = 2 and k = 2 ).

for instance a tour that guarantees 2-edge-connectivity or a clique.Then, the remaining nodes of the PoP, which model access nodesare connected to the PoPs backbone nodes using at least k edges.Using k 2 guarantees redundancy in case of failure ( n 2 isalso needed).

NOTE: if the degree of backbone nodes in the PoP is too high,the methodology could be improved to add an intermediate layer of aggregation.

4.4.3 Building the backbone topologyOnce each PoP has been generated, the next step consists in con-

necting them together. In the real world, the PoPs are usually inter-connected with multiple links in the backbone. In [22] for instance,Iannaccone et al indicate that in the Sprint backbone, each PoP isconnected to a subset of the other PoPs. A full-mesh would obvi-ously be too expensive. On the other hand, a simple star-topologyis not recommended.

In practice, network designers rely on a variety of mesh-generationheuristics [31, 6, 21]. Their operation usually consists in buildinga seed network topology with built-in requirements such as a max-imum number of hop separating each pair of nodes or a minimumconnectivity. Then, they proceed iteratively, adding or removing

links in order to satisfy additional constraints (path-diversity, link utilization for a given demand prediction). This part is often time-consuming due to the evaluation of many metrics performed at eachiteration. At the end, the heuristic leads to a close to optimum meshdesign.

In our methodology, we consider only the rst step of network design heuristics to generate the backbone. The rst advantage isthat the seed topology can be computed quickly. The disadvantageis that we do not produce optimal topologies. However, to build asynthetic model of the Internet, we need to generate a large num-ber of topologies. We need not produce optimal designs for each

domain.The rst backbone design heuristic we consider is known as

MENTOR [6] and builds a hybrid minimum spanning tree/shortest-path tree (MST-SPT). The idea behind MENTOR is to nd a cen-tral node from which to start and use a Dijkstra approach where thelabels of nodes are not only the distance from the root, but a lin-ear combination of the distance from the root (start) node and the

distance from the previou node. The second component pushes tominimize the total network span. The linear combination is drivenby a parameter which varies between 0 and + . With = 0 ,the heuristic generates a MST while with = 1 , the resulting treeis close to an SPT. This heuristic has similarities with the Heuristi-cally Optimized Trade-offs (HOT) proposed by Fabrikant et al [14].In the HOT approach, nodes arrive uniformly at random in the unitsquare. The new nodes attach to a previously arrived node based onthe same combination of distances than in MENTOR. The differ-ence with MENTOR is that it relies on nodes whose geographicallocation is known in advance. In MENTOR the starting node is thecentroid of the set of vertices.

Since trees are weak networks, another heuristic called MEN-Tour [6] can be used. This heuristics directly builds a 2-edge-connected network by computing a minimum length hamiltoniancycle. Since computing a minimum length hamiltonian cycle is anNP complete problem, we rely on a Traveling Salesman Problem(TSP) approximation heuristic to compute the cycle. We use the furthest-neighbor heuristic. This heuristic starts with a tour thatvisits two vertices which are furthest apart. The next vertex to beinserted is the one that increases the length of the current tour themost when this vertex is inserted in the best position on the currenttour. The rationale behind the furthest insertion heuristic is thatsome vertices will be expensive to insert. What are the guaranteesin term of tour length ? Higher bound on the length compared to theoptimum ? NOTE: the furthest-insertion heuristic does not guar-antee that two edges wil not cross. The only construction heuristicthat guarantees this is the sweep heuristic.

Another way to produce a 2-edge-connected network is the TwoTrees method [21] which builds 2 MSTs. The TwoTrees methodwhich is due to [31] relies on the combination of two trees to forma network. Good candidate trees are MSTs. The method we havechosen starts with the MST on the complete set of edges E . Thenit removes the edges of the rst tree from E and searches in theresulting graph a second MST which is thus edge-disjoint with therst MST. The produced graph is the union of both MSTs. Notethat other trees may be used to generate such networks [21].

Finally an interesting mesh generation techniqueconsists in com-puting a Delaunay triangulation of the backbone nodes. A De-launay triangulation is a special type of triangulation graph. It is


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unique and it is the dual of the Vorono diagram. The Vorono dia-gram is a partition of the space into polygons called sites. Each sitecontains a single vertex and covers the area of points that are closerto the vertex than to any other vertex. The Delaunay triangulationis a graph that connects two vertices together if their sites in theVorono diagram are adjacent. It therefore connects the sites thatare close to each other. A Delaunay triangulation can be computedefciently (typicaly in O (n.log (n )) [10]). The Delaunay triangu-lation also has interesting properties. For instance, it contains theMST. Using a Delaunay triangulation produces a topology with al-ternate paths between nodes, while minimizing the number of suchpaths. This is an efcient way of obtaining a cost-effective topol-ogy with redundancy.

For clarity reasons, we show in Fig. 3 a visual illustration of how each method performs. The various methods were applied toa randomly generated set of 20 vertices covering Australia.

4.4.4 Assigning IGP weightsAfter the topology generation step, we assign IGP weights to

the links. The IGP weights assignment will inuence the selectionof the paths used to cross the network. Strangely, this step hasreceived little attention in the topology generators currently in use[29, 7].

In real world networks, different assignment schemes are used.There are two main schemes and a lot of variations. The rst com-mon scheme consists in assigning to each link an IGP weight thatis proportional to the link propagation delay or the link mileage .In a least-weight routing scheme, this weights assignment leads tothe selection of intradomain paths with the smallest delay. This isthe scheme deployed in the Abilene backbone. In Fig. 4 we show ascatterplot of the IGP weights versus the links mileage. There is aclear correlation between the IGP weights and the links mileage inthe Abilene network.

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

I G P w e

i g h t s

Distance (Kms)

AbileneAbilene [fitted]

f(x)=x

Figure 4: Scatterplot of IGP weights versus links mileage inAbilene.

Another common practice is to assign the IGP weight of a link based on the inverseof its capacity . This assignment is also knownas the CISCO default metric and it is supposed to favour Equal-Cost-Multi-Path (ECMP). It leads to intradomain paths using thehighest bandwidth links. In backbone networks, most link capaci-ties are high and similar. In this case, a least-weight routing schemebehaves as minimum-hop routing. In real world networks, the IGPweights deriver from the inverse of the capacity are often manuallytuned. This is the case in the GEANT backbone. We show in Fig. 5the scatterplot of the IGP weights versus the links capacities. We

also show the inverse of capacity function ( 1012

C ) in order to com-pare. We observe that the GEANT links have 3 different capacities:155Mbps, 2.4Gbps and 10Gbps. For most links, the assigned IGPweight is in conformance with the inverse-capacity scheme exceptfor two links.

1e+00

1e+01

1e+02

1e+03

1e+04

1e+05

1e+06

1e+08 1e+09 1e+10

I G P w e

i g h t s

Bandwidth (Mbps)

GeantCISCO default

Figure 5: Scatterplot of IGP weights versus link capacity in

GEANT.

In addition to the above schemes, some operators use smarterassignments such as AT&Ts IGP weight optimization method pro-posed by Fortz et al [18] that minimizes the link utilization. An-other possibility is to rely on the method proposed by Nucci et al[34] to optimize IGP weights but without having a negative impacton the IP fast-restoration techniques [22].

In our methodology, IGP weights can be assigned a constantvalue or they can be based on the link mileage or on the inverseof the links capacities. In the rst case, all the links will have thesame IGP weight and shortest-path routing will compute minimum-hop paths. The third assignment, based on the inverse of capacities,requires that link capacities be assigned in advance. In the future,we could also rely on Fortzs IGP-WO implemented in the TOTEMtoolbox [46]. Using this method would require the links capacitiesas well as the trafc matrix.

4.4.5 Assigning capacitiesIn an optional step, capacities can be assigned to the links. The

approach of current topology generators consists in assigning linkscapacities in a random manner. In BRITE [29] for instance, band-width can be assigned to links according to uniform, exponential orPareto distributions. Random assignment of link capacities is inter-esting since it allows to generate many different assignments. How-ever, it is very unlikely to produce link capacity assignments thatare realistic. In real network design, link capacities are assignedin order to accomodate a trafc demand between the nodes of the network. In [33] for instance, Norden has evaluated a new QoS

routing algorithm. For this purpose, he designed synthetic topolo-gies and relied on a real network design method proposed by Fin-gerhut et at [17] to compute the bandwidth of the links. The methodcomputes the links capacities that are sufcient to carry a trafc de-mand that satises predened constraints. The method uses linearprogramming in order to solve the assignment.

In our methodology, we assigned the link capacities in order toensure that the demand matrix can be accomodated. For this pur-pose, we do not rely on linear programming, but we compute theAll-Pairs Shortest Paths (APSP) and we simulate the forwarding of trafc demand between all pairs of nodes in order to compute the


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(a) MST (b) hybrid MST-SPT ( = 0 . 7 ) (c) hybrid MST-SPT ( = 0 . 3 )

(d) minimum length hamiltonian cycle (e) two disjoint MSTs (f) Delaunay triangulation

Figure 3: Various mesh designs for a 20-nodes topology located in Australia.

utilization of each link. If there are multiple equal-cost paths, thevolume of the demand is splitted equally among the available pathsas in [16]. Based on the computed load of each link, the tool selectsthe suitable capacities.

The utilization of the links is computed based on the computedshortest-paths. The trafc matrix T gives the amount of trafc ex-changed between the nodes. In particular, st gives the volumesent from the source node t to the destination node t .

u,v X( s,t ) st (u, v ) .T st

st(1)

where u,v is the capacity of link (u, v ). The selected capacitymust be higher than the computed load of each link. The possiblelink capacities are selected in a nite set of capacities correspond-ing to technologies in use today (see Fig. 2).

Technology CapacityE3 34 MbpsT3 45 MbpsSTM-1 155 MbpsSTM-4/OC-12 622 MbpsGigabit Ethernet 1 GbpsSTM-16/OC-48 2.4 GbpsSTM-64/OC-192 10 Gbps

Table 2: Capacities of links.

In addition, the link capacity can be assigned so as to limit themaximum link utilization to a predened level . This correspondsto real world operational practice. For instance, links are oftengiven a capacity such that the load will be 40 to 50 % [45]. Therationale behind this practice is to keep spare capacity in order

to accomodate the variations of the trafc demand as well as itsevolution. In the future, we plan to simulate the single-link/routerfailures and compute the capacity required to accomodate all (or asubset of) the failures. This is what is implemented in commercialnetwork design tools such as WANDL IP/MPLSView [24].

4.5 Comparison of the mesh generation tech-niques

In order to compare the above mesh generation techniques, weapplied them to different sets of vertices. The two rst sets are realworld networks: Abilene, the US research backbone, and GEANT,

the european research backbone. The two second sets are synthetic.They are composed of vertices whose coordinates were generateduniformly at random. The rst synthetic network is composed of 20nodes placed on the Australian continent (Australia-20). The sec-

ond set is composed of 50 nodes placed in North America (North-America-50).We generated the following designs for each set ofvertices. First,

a tour, that we call TSP. Then, two hybrid MST-SPTs with param-eters = 0 .3 (MENTOR 0.3) and = 0 .7 (MENTOR 0.7). Thethird class of mesh is based on the TwoTrees heuristic (TwoTrees).Finally, we generated a Delaunay triangulation of the vertices (De-launay). In these topologies, the weight of each link is set accordingto the link length.

In Fig. 6, we show a measure of the length of the shortest paths inthe different generated meshes. On the x-axis, we show the lengthof the paths. On the y-axis, we show the cumulative fraction of paths that have the corresponding length. A rst observation is thatfor this metric the heuristics can be sorted starting from the bestand ending with the worst. The Delaunay triangulation provides

the best results, then the TwoTrees, followed by the MST-SPTs andthe worst results are provided by the TSP.

For the Abilene and GEANT backbones, we can compare thesynthetic meshes with the original networks. The average path-length in the Abilene backbone is 2385.7 kms with a standard de-viation of 1296.9 kms. The maximum path lengths is 5029.2 kms.The maximum path length gives an idea of an upper bound on thepropagation delay in the network. The Delaunay triangulation pro-vides an average shortest path length equal to 2056.9 kms with astd. dev. of 1077.8 kms. The maximum length is 4126.5 kms. Onthe other hand, the TSP heuristic leads to an average shortest pathlength of 3198.8 kms with a std. dev. of 1664.4 kms. The maxi-mum length is 5811.4 kms. If short delays are an objective of thedesign, the TSP heuristics should be avoided. When the network contains a larger number of nodes, the results of the TSP are goingfurther apart from the other heuristics (see North-America-50).

In GEANT, the average path length is 2166.6 kms with a stan-dard deviation of 1733.3 kms. The larger deviation can be ex-plained by the fact that the GEANT backbone contains two linksthat cross the atlantic ocean. BLABLABLA

In Fig. 7, we show a measure of thepath-diversity in the differentgenerated meshes. The lowest path diversity is obtained with theMST-SPT heuristic since it builds trees. The offered path-diversityin this case is limited to 1. Then, the TSP offers a path-diversityof 2 with one path clockwise and another counterclockwise. The


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MENTOR heuristic provides a path-diversityThe evaluation performed in this section helps to select which

mesh generation heuristic is suitable for what objective. For in-stance, if we want a minimum cost network with good delay char-acteristics and if we do not care about the resilience, the MST-SPTapproach is suitable. If we need resilience and do not care about theperformance, a tour can be used. If resilience and performance mat-ter, the TwoTrees approach can be used since it provides short paths

between any pair of vertices. In addition, it is 2-edge-connectedsince the minimum edge-cut in a TwoTree-generated mesh contains2 edges. Such a network is resilient to a single link failure. Finally,if path diversity is required, the Delaunay triangulation providesperformance and a high path diversity. If the network cost matter,the TwoTrees approach is preferable over the Delaunay triangula-tion since the latter contains a larger number of edges.


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5. AN EXPERIMENTAL INTERNET TOPOL-OGY

In this section, we describe an experimental router-level Internettopology designed based on the methodology introduced in Sec-tion 4. This topology is not a model of the real Internet topology.This model can not be used for the purpose of reproducing howinterdomain routing and interdomain trafc engineering behave in

the real Internet.It is rather a model capturing some aspects of theInternet topology such as the geographical spread of routers, theredundancy of peering links, peering policies and router-level in-tradomain topologies. It can be used to study how these character-istics impact routing and trafc engineering techniques.

The section is organized as follows. We rst describe the datasetsthat we used to build the topology in Section ?? . Then, we describeour methodology in Section ?? .


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5.1 Geographic location of routersThe rst step towards the construction of our router-level Internet

topology consists in positionnning the routers on the earth. A char-acterization of the geographic location of routers was performedby Lakhina et al [25]. However, no model exists. BRITE [29] pro-vides a mean to place routers at random on a square map using auniform or a pareto distributions. However, it is unsure whether ornot the resulting geographical distribution has similarities with thereal world.

We rely on a dataset providing a mapping between ranges of IPaddresses and geographic coordinates (latitude and longitude).This dataset was obtained by a geolocation technique [35]. Suchtechnique relies on a mix of whois databases requests (see also[32]), hostname based mapping and various other heuristics to de-termine with more or less accuracy the location of an Internet host.According to [35], a single technique alone is not sufcient, butthe combination of whois, hostname and ad-hoc information worksquite well. The potential uses of geographic mapping include con-tent customization, targeted advertising and struggle against creditcard fraud. A lot of commercial companies are selling such databasestoday. Among them, we opted for MaxMind [1] which claims foran high accuracy 2. The database we use is dated from the 6thof June, 2004 and it contains 1873457 ranges of IP addresses in118489 geographical locations.

With this dataset, we do not obtain the location of routers but thelocation of Internet hosts. However, we rely on the fact that blocksof IP addresses represent networks that are connected to a PoP of an ISP. Groups of IP addresses that belong to the same domain andthat are located at the same place constitute a PoP for this domain.

5.2 Geographic coverage of domainsWe need to identify for each block of IP addresses by which do-

main it is owned. We rely on a BGP routing table dump for this

2In addition to affordable prices for education

Figure 11: Plot of the points-of-presence on a world map.

purpose. This routing table provides us with a mapping between IPprexes and AS-Paths. We take the last AS in the AS-Path to re-trieve the origin AS of an IP prex 3 . With this information, we areable to nd the origin AS of prexes that contain the IP addressesranges found in the geolocation dataset. The BGP routing tabledump we use was collected by the RouteViews project [30] andis dated from the 5th of June, 2004 and contains 139527 different

prexes originated by WWW different ASes. NOTE: say how many origin AS were found + say how manylocations were found in each AS (median, p-5 and p-95 or distribu-tion)

5.3 Domain topologiesBased on the geolocation dataset and on a BGP routing table

3In the case of aggregated routes with an AS-Path that does notend with an AS_SEQUENCE segment, we are not able to nd theorigin of the route. This concerns only XXX percent of the routingtable


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dump, we are able to nd for each domain a set of N PoPs. Weknow the geographical location of each PoP. We apply the method-ology described in Section 4 to generate a router-level topology foreach domain.

We use the following parameters. For each domain, we groupits N locations in K = N S clusters which leads to clusters with anaverage size of S . We arbitrarily choose to use S = 5 , but othervalues are possible. Then, we generated the structure of each PoPusing the methodology of Section 4.4.3. The parameters we useare n = 2 backbone routers in each PoP and a redundancy factork = 2 . This ensures a robust PoP design. To connect the PoPstogether, we choose the Delaunay triangulation since it providesa performant, redundant network at a reasonable cost. The othermesh generation heuristics described in Section 4.4.3 can also beused. Then, we assign IGP weights based on the links mileage. Fi-nally, we assign capacities. Since we do not have a trafc demand,we choose to assign backbone links an high capacity h and ac-cess links a lower capacity l . We arbitrarily choose 10Gbps and155Mbps as values for h and l respectively.

5.4 Interdomain peeringsIn order to connect the domains together, we need to know for

each pair of domains if they have a peering together. In this case,we also need to know if it is a customer-provider or peer-to-peer re-lationship. We use an AS-level topology inferred by Subramanianet al [40]. This dataset contains the interdomain relationships thatexist between Internet domains. We are aware of the limitations of such dataset [12]. In particular the utilization of a small set of van-tage points located mostly in the core of the Internet misses a largenumber of shared-cost and backup peerings. Dimitropoulos et alhave recently proposed a new approach to the generation of syn-thetic AS-level topologies with embedded policies [13]. Anotherpossibility would be to rely on an AS-level topology generator thatproduces an hierachy of domains such as GHITLE [11].

NOTE: Such data can not be produced by BRITE. GT-ITM2 [8]is supposed to produce such policies but it is still not available publicly.

In addition, each time two domains have a peering relationship,we need to decide how many peering links they have between eachother and where these links are connected. We decided to deter-mine the number of interdomain links N ij based on the sizes of thedomains, N i and N j . We use the following formula

N ij = 1 + ( N 1). N i .N j(max i N i )2 (2)This formula guarantees that 1 N ij N . We choose arbitrarilyN = .

To place these links, we rely on the assumption that two domainswill preferably connect at places where both are present. Our al-gorithm to select the endpoints of the N interdomain links is asfollows. We start with N links to select. In the rst iteration, we

search among the N i N j pairs of routers the shortest link (u 1 , v1 ).Then, we remove from the set of possible endpoints the vertices u1and v1 . We start a second iteration, and so on until N links areplaced.

NOTE: the above algorithm has limitations. First, the order inwhich links are selected has an impact on the solution found. It might be better to select a slightly longer link at rst to reach a bet-ter solution. I wonder if this is a well-known combinatorial prob-lem. Second, the algorithm does not take the geographical spread of the interconnections into account. This is probably one of theobjectives of domains.

Domain i Domain j

Figure 12: Interconnection of two domains.

5.4.1 Internal BGP setupIn addition to the model of the physical or layer-3 topology, the

evaluation of interdomain routing protocols also requires a modelof the logical topology. The physical model represents the phys-ical (or layer-3) links that exist between routers. In contrast, thelogical topology denes how the routers talk to each other and ex-change routing information. The logical topology can be detailedin the logical topology used inside domains and the logical topol-ogy used between domains. Typicaly, the internal logical topologymodels the iBGP sessions between routers while the external topol-ogy models the eBGP sessions. The internal and external logicaltopologies follow different design rules.

The logical topology inside a domain strongly differs from thephysical (or layer-3) topology. There are two typical congurationsof BGP within a domain. The rst one is a full-mesh of iBGPsessions, meaning that each router has an iBGP session with allthe other routers. Fig. 13 shows an example of a simple network topology composed of three PoPs on the left and the internal logicaltopology for the same network if a full-mesh of iBGP sessions isused. The iBGP full-mesh can be modeled as a clique of undirectededges.

The second common logical topology within a domain is aniBGP hierarchy. In such a topology, not all routers and not all iBGPsessions are equal. There are special routers named route-reectorsand special iBGP sessions which are sessions to client routers. Thespecial client iBGP sessions are directed. The route-reectors areallowed to propagate over a client iBGP session routes receivedover another iBGP session. A variation of this topology is some-times deployed in real networks. In this variation, the client routersare connected together in a full-mesh of iBGP sessions. Both topolo-gies are illustrated in Fig. 14.

The external part of the logical topology follows the links of thephysical topology. For each link between two domains in the phys-ical topology, there will be an edge in the logical topology, repre-senting an eBGP session. The difference compared to the internallogical topology is that policies are enforced on the external links.

The policies enforced on the external logical links depend onthe economical relationships between the domains. These rela-tionships can be grossly categorized in two types [19]: provider-

customer and peer-to-peer relationships. The rst type of relation-ship is used between a provider and a customer domains. The cus-tomer buys connectivity from its provider and receives from thisprovider routes towards all the Internet destinations. In addition,the providers advertises to the whole Internet the networks of thecustomer. The second type of relationship occurs between two do-mains that have a private peering and that share its cost. Bothdomains will usually only advertise the routes towards their ownclients on this peering in order to avoid to provide transit for Inter-net routes to the peer domain. In addition, the domains having apeer-to-peer relationship will not advertise to their provider


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$$$

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sibling relationshippeer-to-peer relationship

Figure 15: Interdomain relationships.

The above relationships can be implemented using policies on

the eBGP sessions. Each type of relationship denes a differentpolicy.

In addition to the policies allowing or preventing transit, Internetdomains also use preference settings. These preferences dene apolitical ranking on the routes. A typical setting is to prefere theroutes learned from a customer over the routes received from a peeror a provider. The rational behind this preference is that using theroute received by a customer does not cost money. For the samereason, the routes received from a peer are also prefered over theroutes received from a provider. This denes a local ranking of routes based on the types of relationships: customer routes > peerroutes > provider routes.

NOTE: the model of interdomain relationships from Gao et al iscoarse. (1) It is not unusal to have domains that maintain differ-ent relationships over different peering links. (2) In addition, other policies are enforced. For instance, research backbone networkssuch as Abilene only redistribute routes towards research and edu-cation networks. Other local policies are also possible (to providebackup routes for instance). (3) Finally, policies related to trafcengineering are also enforced.

6. CONCLUSIONIn this chapter, we have described a pragmatic methodology to

build router-level Internet topologies. In the rst part of the chap-ter, we focused on the generation of a single domain topology. We

presented an original methodology which, in contrast with tradi-

tional topology generators, relies on network design heuristics in-stead of probabilistic models. We described 4 different network design heuristics and we compared them based on real world net-works as well as synthetic sets of vertices. We used different met-rics to examine the performance obtained with each heuristic. Tocite two heuritics, we concluded that the hybrid MST-SPT heuristicis suitable to build low-cost and performant networks without ro-bustness. On the other hand, a Delaunay triangulation produces aperformant network that is resilient to the failure of links and nodes.In addition, we present solutions to the assignment of IGP weightsand capacities to the network links.

In the second part, we applied our router-level topology gener-ator to the construction of an Internet-like toplogy. This topologycaptures different aspects of the real world Internet topology suchas the redundancy of peering links, peering policies, geographicspread of routers and router-level domain topologies. We describedhow to build this topology from 3 datasets obtained by measure-ment in the real Internet. This topology is more detailled thantopologies obtained from probabilistic models. In addition, it ispossible to vary its characteristics and study their impact on theperformance of interdomain routing and trafc engineering.

NOTE: - talk about links croissing ocean (Atlantic= pond/millpond)- talk about operational practice for iBGP hierarchy: if network over multiple continents, use top-level RRs on both sides of theocean instead of having all major locations on the top-level mesh.


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For the modeling, this may mean that an additional level of RRs isrequired. See RIPE-49 BGP network design...

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